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d33397aa6516d73e47e456d2aeb0f71fdd29ca33
gonum/graph/community/louvain_undirected_test.go
Brendan Tracey d33397aa65 all: change import paths
2017-05-23 00:03:03 -06:00

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// Copyright ©2015 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package community
import (
"math"
"math/rand"
"reflect"
"sort"
"testing"
"gonum.org/v1/gonum/floats"
"gonum.org/v1/gonum/graph"
"gonum.org/v1/gonum/graph/internal/ordered"
"gonum.org/v1/gonum/graph/simple"
)
var communityUndirectedQTests = []struct {
name string
g []set
structures []structure
wantLevels []level
}{
// The java reference implementation is available from http://www.ludowaltman.nl/slm/.
{
name: "unconnected",
g: unconnected,
structures: []structure{
{
resolution: 1,
memberships: []set{
0: linksTo(0),
1: linksTo(1),
2: linksTo(2),
3: linksTo(3),
4: linksTo(4),
5: linksTo(5),
},
want: math.NaN(),
},
},
wantLevels: []level{
{
q: math.Inf(-1), // Here math.Inf(-1) is used as a place holder for NaN to allow use of reflect.DeepEqual.
communities: [][]graph.Node{
{simple.Node(0)},
{simple.Node(1)},
{simple.Node(2)},
{simple.Node(3)},
{simple.Node(4)},
{simple.Node(5)},
},
},
},
},
{
name: "small_dumbell",
g: smallDumbell,
structures: []structure{
{
resolution: 1,
// community structure and modularity calculated by java reference implementation.
memberships: []set{
0: linksTo(0, 1, 2),
1: linksTo(3, 4, 5),
},
want: 0.357, tol: 1e-3,
},
{
resolution: 1,
memberships: []set{
0: linksTo(0, 1, 2, 3, 4, 5),
},
// theoretical expectation.
want: 0, tol: 1e-14,
},
},
wantLevels: []level{
{
q: 0.35714285714285715,
communities: [][]graph.Node{
{simple.Node(0), simple.Node(1), simple.Node(2)},
{simple.Node(3), simple.Node(4), simple.Node(5)},
},
},
{
q: -0.17346938775510204,
communities: [][]graph.Node{
{simple.Node(0)},
{simple.Node(1)},
{simple.Node(2)},
{simple.Node(3)},
{simple.Node(4)},
{simple.Node(5)},
},
},
},
},
{
name: "zachary",
g: zachary,
structures: []structure{
{
resolution: 1,
// community structure and modularity from doi: 10.1140/epjb/e2013-40829-0
memberships: []set{
0: linksTo(0, 1, 2, 3, 7, 11, 12, 13, 17, 19, 21),
1: linksTo(4, 5, 6, 10, 16),
2: linksTo(8, 9, 14, 15, 18, 20, 22, 26, 29, 30, 32, 33),
3: linksTo(23, 24, 25, 27, 28, 31),
},
// Noted to be the optimal modularisation in the paper above.
want: 0.4198, tol: 1e-4,
},
{
resolution: 0.5,
// community structure and modularity calculated by java reference implementation.
memberships: []set{
0: linksTo(0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 16, 17, 19, 21),
1: linksTo(8, 14, 15, 18, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33),
},
want: 0.6218, tol: 1e-3,
},
{
resolution: 2,
// community structure and modularity calculated by java reference implementation.
memberships: []set{
0: linksTo(14, 18, 20, 22, 32, 33, 15),
1: linksTo(0, 1, 11, 17, 19, 21),
2: linksTo(2, 3, 7, 9, 12, 13),
3: linksTo(4, 5, 6, 10, 16),
4: linksTo(24, 25, 28, 31),
5: linksTo(23, 26, 27, 29),
6: linksTo(8, 30),
},
want: 0.1645, tol: 1e-3,
},
},
wantLevels: []level{
{
q: 0.4197896120973044,
communities: [][]graph.Node{
{simple.Node(0), simple.Node(1), simple.Node(2), simple.Node(3), simple.Node(7), simple.Node(11), simple.Node(12), simple.Node(13), simple.Node(17), simple.Node(19), simple.Node(21)},
{simple.Node(4), simple.Node(5), simple.Node(6), simple.Node(10), simple.Node(16)},
{simple.Node(8), simple.Node(9), simple.Node(14), simple.Node(15), simple.Node(18), simple.Node(20), simple.Node(22), simple.Node(26), simple.Node(29), simple.Node(30), simple.Node(32), simple.Node(33)},
{simple.Node(23), simple.Node(24), simple.Node(25), simple.Node(27), simple.Node(28), simple.Node(31)},
},
},
{
q: 0.39907955292570674,
communities: [][]graph.Node{
{simple.Node(0), simple.Node(1), simple.Node(2), simple.Node(3), simple.Node(7), simple.Node(11), simple.Node(12), simple.Node(13), simple.Node(17), simple.Node(19), simple.Node(21)},
{simple.Node(4), simple.Node(10)},
{simple.Node(5), simple.Node(6), simple.Node(16)},
{simple.Node(8), simple.Node(9), simple.Node(14), simple.Node(15), simple.Node(18), simple.Node(20), simple.Node(22), simple.Node(26), simple.Node(29), simple.Node(30), simple.Node(32), simple.Node(33)},
{simple.Node(23), simple.Node(24), simple.Node(25), simple.Node(27), simple.Node(28), simple.Node(31)},
},
},
{
q: -0.04980276134122286,
communities: [][]graph.Node{
{simple.Node(0)},
{simple.Node(1)},
{simple.Node(2)},
{simple.Node(3)},
{simple.Node(4)},
{simple.Node(5)},
{simple.Node(6)},
{simple.Node(7)},
{simple.Node(8)},
{simple.Node(9)},
{simple.Node(10)},
{simple.Node(11)},
{simple.Node(12)},
{simple.Node(13)},
{simple.Node(14)},
{simple.Node(15)},
{simple.Node(16)},
{simple.Node(17)},
{simple.Node(18)},
{simple.Node(19)},
{simple.Node(20)},
{simple.Node(21)},
{simple.Node(22)},
{simple.Node(23)},
{simple.Node(24)},
{simple.Node(25)},
{simple.Node(26)},
{simple.Node(27)},
{simple.Node(28)},
{simple.Node(29)},
{simple.Node(30)},
{simple.Node(31)},
{simple.Node(32)},
{simple.Node(33)},
},
},
},
},
{
name: "blondel",
g: blondel,
structures: []structure{
{
resolution: 1,
// community structure and modularity calculated by java reference implementation.
memberships: []set{
0: linksTo(0, 1, 2, 3, 4, 5, 6, 7),
1: linksTo(8, 9, 10, 11, 12, 13, 14, 15),
},
want: 0.3922, tol: 1e-4,
},
},
wantLevels: []level{
{
q: 0.39221938775510207,
communities: [][]graph.Node{
{simple.Node(0), simple.Node(1), simple.Node(2), simple.Node(3), simple.Node(4), simple.Node(5), simple.Node(6), simple.Node(7)},
{simple.Node(8), simple.Node(9), simple.Node(10), simple.Node(11), simple.Node(12), simple.Node(13), simple.Node(14), simple.Node(15)},
},
},
{
q: 0.34630102040816324,
communities: [][]graph.Node{
{simple.Node(0), simple.Node(1), simple.Node(2), simple.Node(4), simple.Node(5)},
{simple.Node(3), simple.Node(6), simple.Node(7)},
{simple.Node(8), simple.Node(9), simple.Node(10), simple.Node(12), simple.Node(14), simple.Node(15)},
{simple.Node(11), simple.Node(13)},
},
},
{
q: -0.07142857142857144,
communities: [][]graph.Node{
{simple.Node(0)},
{simple.Node(1)},
{simple.Node(2)},
{simple.Node(3)},
{simple.Node(4)},
{simple.Node(5)},
{simple.Node(6)},
{simple.Node(7)},
{simple.Node(8)},
{simple.Node(9)},
{simple.Node(10)},
{simple.Node(11)},
{simple.Node(12)},
{simple.Node(13)},
{simple.Node(14)},
{simple.Node(15)},
},
},
},
},
}
func TestCommunityQUndirected(t *testing.T) {
for _, test := range communityUndirectedQTests {
g := simple.NewUndirectedGraph(0, 0)
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if !g.Has(simple.Node(u)) {
g.AddNode(simple.Node(u))
}
for v := range e {
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
}
}
for _, structure := range test.structures {
communities := make([][]graph.Node, len(structure.memberships))
for i, c := range structure.memberships {
for n := range c {
communities[i] = append(communities[i], simple.Node(n))
}
}
got := Q(g, communities, structure.resolution)
if !floats.EqualWithinAbsOrRel(got, structure.want, structure.tol, structure.tol) && !math.IsNaN(structure.want) {
for _, c := range communities {
sort.Sort(ordered.ByID(c))
}
t.Errorf("unexpected Q value for %q %v: got: %v want: %v",
test.name, communities, got, structure.want)
}
}
}
}
func TestCommunityDeltaQUndirected(t *testing.T) {
tests:
for _, test := range communityUndirectedQTests {
g := simple.NewUndirectedGraph(0, 0)
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if !g.Has(simple.Node(u)) {
g.AddNode(simple.Node(u))
}
for v := range e {
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
}
}
rnd := rand.New(rand.NewSource(1)).Intn
for _, structure := range test.structures {
communityOf := make(map[int]int)
communities := make([][]graph.Node, len(structure.memberships))
for i, c := range structure.memberships {
for n := range c {
communityOf[n] = i
communities[i] = append(communities[i], simple.Node(n))
}
sort.Sort(ordered.ByID(communities[i]))
}
before := Q(g, communities, structure.resolution)
l := newUndirectedLocalMover(reduceUndirected(g, nil), communities, structure.resolution)
if l == nil {
if !math.IsNaN(before) {
t.Errorf("unexpected nil localMover with non-NaN Q graph: Q=%.4v", before)
}
continue tests
}
// This is done to avoid run-to-run
// variation due to map iteration order.
sort.Sort(ordered.ByID(l.nodes))
l.shuffle(rnd)
for _, target := range l.nodes {
got, gotDst, gotSrc := l.deltaQ(target)
want, wantDst := math.Inf(-1), -1
migrated := make([][]graph.Node, len(structure.memberships))
for i, c := range structure.memberships {
for n := range c {
if n == target.ID() {
continue
}
migrated[i] = append(migrated[i], simple.Node(n))
}
sort.Sort(ordered.ByID(migrated[i]))
}
for i, c := range structure.memberships {
if i == communityOf[target.ID()] {
continue
}
connected := false
for n := range c {
if g.HasEdgeBetween(simple.Node(n), target) {
connected = true
break
}
}
if !connected {
continue
}
migrated[i] = append(migrated[i], target)
after := Q(g, migrated, structure.resolution)
migrated[i] = migrated[i][:len(migrated[i])-1]
if after-before > want {
want = after - before
wantDst = i
}
}
if !floats.EqualWithinAbsOrRel(got, want, structure.tol, structure.tol) || gotDst != wantDst {
t.Errorf("unexpected result moving n=%d in c=%d of %s/%.4v: got: %.4v,%d want: %.4v,%d"+
"\n\t%v\n\t%v",
target.ID(), communityOf[target.ID()], test.name, structure.resolution, got, gotDst, want, wantDst,
communities, migrated)
}
if gotSrc.community != communityOf[target.ID()] {
t.Errorf("unexpected source community index: got: %d want: %d", gotSrc, communityOf[target.ID()])
} else if communities[gotSrc.community][gotSrc.node].ID() != target.ID() {
wantNodeIdx := -1
for i, n := range communities[gotSrc.community] {
if n.ID() == target.ID() {
wantNodeIdx = i
break
}
}
t.Errorf("unexpected source node index: got: %d want: %d", gotSrc.node, wantNodeIdx)
}
}
}
}
}
func TestReduceQConsistencyUndirected(t *testing.T) {
tests:
for _, test := range communityUndirectedQTests {
g := simple.NewUndirectedGraph(0, 0)
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if !g.Has(simple.Node(u)) {
g.AddNode(simple.Node(u))
}
for v := range e {
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
}
}
for _, structure := range test.structures {
if math.IsNaN(structure.want) {
continue tests
}
communities := make([][]graph.Node, len(structure.memberships))
for i, c := range structure.memberships {
for n := range c {
communities[i] = append(communities[i], simple.Node(n))
}
sort.Sort(ordered.ByID(communities[i]))
}
gQ := Q(g, communities, structure.resolution)
gQnull := Q(g, nil, 1)
cg0 := reduceUndirected(g, nil)
cg0Qnull := Q(cg0, cg0.Structure(), 1)
if !floats.EqualWithinAbsOrRel(gQnull, cg0Qnull, structure.tol, structure.tol) {
t.Errorf("disagreement between null Q from method: %v and function: %v", cg0Qnull, gQnull)
}
cg0Q := Q(cg0, communities, structure.resolution)
if !floats.EqualWithinAbsOrRel(gQ, cg0Q, structure.tol, structure.tol) {
t.Errorf("unexpected Q result after initial reduction: got: %v want :%v", cg0Q, gQ)
}
cg1 := reduceUndirected(cg0, communities)
cg1Q := Q(cg1, cg1.Structure(), structure.resolution)
if !floats.EqualWithinAbsOrRel(gQ, cg1Q, structure.tol, structure.tol) {
t.Errorf("unexpected Q result after second reduction: got: %v want :%v", cg1Q, gQ)
}
}
}
}
var localUndirectedMoveTests = []struct {
name string
g []set
structures []moveStructures
}{
{
name: "blondel",
g: blondel,
structures: []moveStructures{
{
memberships: []set{
0: linksTo(0, 1, 2, 4, 5),
1: linksTo(3, 6, 7),
2: linksTo(8, 9, 10, 12, 14, 15),
3: linksTo(11, 13),
},
targetNodes: []graph.Node{simple.Node(0)},
resolution: 1,
tol: 1e-14,
},
{
memberships: []set{
0: linksTo(0, 1, 2, 4, 5),
1: linksTo(3, 6, 7),
2: linksTo(8, 9, 10, 12, 14, 15),
3: linksTo(11, 13),
},
targetNodes: []graph.Node{simple.Node(3)},
resolution: 1,
tol: 1e-14,
},
{
memberships: []set{
0: linksTo(0, 1, 2, 4, 5),
1: linksTo(3, 6, 7),
2: linksTo(8, 9, 10, 12, 14, 15),
3: linksTo(11, 13),
},
// Case to demonstrate when A_aa != k_a^𝛼.
targetNodes: []graph.Node{simple.Node(3), simple.Node(2)},
resolution: 1,
tol: 1e-14,
},
},
},
}
func TestMoveLocalUndirected(t *testing.T) {
for _, test := range localUndirectedMoveTests {
g := simple.NewUndirectedGraph(0, 0)
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if !g.Has(simple.Node(u)) {
g.AddNode(simple.Node(u))
}
for v := range e {
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
}
}
for _, structure := range test.structures {
communities := make([][]graph.Node, len(structure.memberships))
for i, c := range structure.memberships {
for n := range c {
communities[i] = append(communities[i], simple.Node(n))
}
sort.Sort(ordered.ByID(communities[i]))
}
r := reduceUndirected(reduceUndirected(g, nil), communities)
l := newUndirectedLocalMover(r, r.communities, structure.resolution)
for _, n := range structure.targetNodes {
dQ, dst, src := l.deltaQ(n)
if dQ > 0 {
before := Q(r, l.communities, structure.resolution)
l.move(dst, src)
after := Q(r, l.communities, structure.resolution)
want := after - before
if !floats.EqualWithinAbsOrRel(dQ, want, structure.tol, structure.tol) {
t.Errorf("unexpected deltaQ: got: %v want: %v", dQ, want)
}
}
}
}
}
}
func TestModularizeUndirected(t *testing.T) {
const louvainIterations = 20
for _, test := range communityUndirectedQTests {
g := simple.NewUndirectedGraph(0, 0)
for u, e := range test.g {
// Add nodes that are not defined by an edge.
if !g.Has(simple.Node(u)) {
g.AddNode(simple.Node(u))
}
for v := range e {
g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
}
}
if test.structures[0].resolution != 1 {
panic("bad test: expect resolution=1")
}
want := make([][]graph.Node, len(test.structures[0].memberships))
for i, c := range test.structures[0].memberships {
for n := range c {
want[i] = append(want[i], simple.Node(n))
}
sort.Sort(ordered.ByID(want[i]))
}
sort.Sort(ordered.BySliceIDs(want))
var (
got *ReducedUndirected
bestQ = math.Inf(-1)
)
// Modularize is randomised so we do this to
// ensure the level tests are consistent.
src := rand.New(rand.NewSource(1))
for i := 0; i < louvainIterations; i++ {
r := Modularize(g, 1, src).(*ReducedUndirected)
if q := Q(r, nil, 1); q > bestQ || math.IsNaN(q) {
bestQ = q
got = r
if math.IsNaN(q) {
// Don't try again for non-connected case.
break
}
}
var qs []float64
for p := r; p != nil; p = p.Expanded().(*ReducedUndirected) {
qs = append(qs, Q(p, nil, 1))
}
// Recovery of Q values is reversed.
if reverse(qs); !sort.Float64sAreSorted(qs) {
t.Errorf("Q values not monotonically increasing: %.5v", qs)
}
}
gotCommunities := got.Communities()
for _, c := range gotCommunities {
sort.Sort(ordered.ByID(c))
}
sort.Sort(ordered.BySliceIDs(gotCommunities))
if !reflect.DeepEqual(gotCommunities, want) {
t.Errorf("unexpected community membership for %s Q=%.4v:\n\tgot: %v\n\twant:%v",
test.name, bestQ, gotCommunities, want)
continue
}
var levels []level
for p := got; p != nil; p = p.Expanded().(*ReducedUndirected) {
var communities [][]graph.Node
if p.parent != nil {
communities = p.parent.Communities()
for _, c := range communities {
sort.Sort(ordered.ByID(c))
}
sort.Sort(ordered.BySliceIDs(communities))
} else {
communities = reduceUndirected(g, nil).Communities()
}
q := Q(p, nil, 1)
if math.IsNaN(q) {
// Use an equalable flag value in place of NaN.
q = math.Inf(-1)
}
levels = append(levels, level{q: q, communities: communities})
}
if !reflect.DeepEqual(levels, test.wantLevels) {
t.Errorf("unexpected level structure:\n\tgot: %v\n\twant:%v", levels, test.wantLevels)
}
}
}
func TestNonContiguousUndirected(t *testing.T) {
g := simple.NewUndirectedGraph(0, 0)
for _, e := range []simple.Edge{
{F: simple.Node(0), T: simple.Node(1), W: 1},
{F: simple.Node(4), T: simple.Node(5), W: 1},
} {
g.SetEdge(e)
}
func() {
defer func() {
r := recover()
if r != nil {
t.Error("unexpected panic with non-contiguous ID range")
}
}()
Modularize(g, 1, nil)
}()
}
func BenchmarkLouvain(b *testing.B) {
src := rand.New(rand.NewSource(1))
for i := 0; i < b.N; i++ {
Modularize(dupGraph, 1, src)
}
}
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